...Evolver[2]

The Surface Evolver is most often referred to as simply Evolver . The name sometimes causes confusion in the materials science community as evolution in the sense of kinetic evolution is not usually implied. Rather the function is evolved by iteratively finding a sequence of discretized shapes which continuously minimize the energy while satisfying imposed constraints. The particular path is determined by the energy minimization algorithm, of which there are several in Evolver . In some cases however, such as grain growth[3], the minimizing algorithm can be chosed so that it simulates the kinetics of motion by mean curvature properly; but this is not the usual case.

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...advantage.

It is also important to note that the imposed symmetry can also impose stability on a system which is unstable to asymmetric deformations of the surface. An example of this follows. When questions of stability are important, it is essential to allow the system to break symmetry. The current example is easily extended for such cases.

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...facet.

Note that for a facet, the there is no contribution to the volume from the three planar parts of the bounding surface 20#20 which are the projections of the edges of the facets to z=0 since 17#17 is normal to those surfaces, and there is no contribution from the "floor" z=0.

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